Computation of the Spatial Distribution of Charge-Carrier Density in Disordered Media

Author:

Nenashev Alexey V.1ORCID,Gebhard Florian1,Meerholz Klaus2,Baranovskii Sergei D.12

Affiliation:

1. Faculty of Physics, Philipps-Universität Marburg, 35032 Marburg, Germany

2. Department für Chemie, Universität zu Köln, Greinstraße 4-6, 50939 Köln, Germany

Abstract

The space- and temperature-dependent electron distribution n(r,T) determines optoelectronic properties of disordered semiconductors. It is a challenging task to get access to n(r,T) in random potentials, while avoiding the time-consuming numerical solution of the Schrödinger equation. We present several numerical techniques targeted to fulfill this task. For a degenerate system with Fermi statistics, a numerical approach based on a matrix inversion and one based on a system of linear equations are developed. For a non-degenerate system with Boltzmann statistics, a numerical technique based on a universal low-pass filter and one based on random wave functions are introduced. The high accuracy of the approximate calculations are checked by comparison with the exact quantum-mechanical solutions.

Funder

Deutsche Forschungsgemeinschaft

Publisher

MDPI AG

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